Check the resistance and voltage at the coils. Also tap on the starter to see if it's sticking. If the V and Ohms are good as the coils (should be 0.8 +/- 0.1) then check voltage from the DME on the coil pins as well as the fuel pump. However, you should be able to hear the pump kick on when you turn on the car. If there is voltage for the pump at the DME, but you don't hear it turn on, check your connections at the pump. If the starter still doesn't engage after tapping, check the starter relay. If it's good inspect the wiring. If that is good, replace the starter or have it tested at the local autozone, kragen, napa, etc.
Check and report back.